{"id":436,"date":"2009-03-28T20:11:36","date_gmt":"2009-03-28T12:11:36","guid":{"rendered":"http:\/\/sinyalee.com\/blog\/?p=436"},"modified":"2009-03-28T20:11:36","modified_gmt":"2009-03-28T12:11:36","slug":"apio-2008-%e8%84%b1%e6%b0%a7%e6%a0%b8%e7%b3%96%e6%a0%b8%e9%85%b8%ef%bc%88dna%ef%bc%89-%e8%a7%a3%e9%a2%98%e6%8a%a5%e5%91%8a","status":"publish","type":"post","link":"https:\/\/sinyalee.com\/blog\/?p=436","title":{"rendered":"APIO 2008 \u8131\u6c27\u6838\u7cd6\u6838\u9178\uff08dna\uff09 \u89e3\u9898\u62a5\u544a"},"content":{"rendered":"

\u9898\u76ee\u4e0e\u6570\u636e\u79fb\u6b65APIO\u5b98\u65b9\u7f51\u7ad9\uff1ahttp:\/\/www.apio.olympiad.org\/<\/a> <\/p>\n

\u9996\u5148\u6211\u5bf9ACGT\u5206\u522b\u6807\u53f7\u4e3a1234\uff0c\u65b9\u4fbf\u540e\u9762\u8ba1\u7b97\u3002\u4e8e\u662f\u628aDNA\u50a8\u5b58\u4e3a\u4e00\u4e2ast\u4e32\uff0c0\u8868\u793aN. <\/p>\n

\u6211\u4eec\u5bf9\u4ed6\u7684\u6240\u8c13\u201c\u8303\u5f0f-j\u201d\u505a\u4e00\u4e0b\u6df1\u5165\u5256\u6790\uff0c\u53d1\u73b0\uff0c\u201c\u8303\u5f0f-j\u201d\u65e0\u975e\u662f\u7b26\u5408st[ x ] > st [ x + 1 ]\u7684x\u7684\u4e2a\u6570\u8981\u5c0f\u4e8ej. <\/p>\n

\u6211\u4eec\u53ef\u4ee5\u8bbe\u8ba1\u72b6\u6001f [ i , be , ik ]\u8868\u793ast [ i ] .. st [ m ]\u4e2d\uff0cst[ i ]\u662fbe\uff0c\u91cc\u9762\u7b26\u5408st[ x ] > st [ x + 1 ]\u7684x\u7684\u4e2a\u6570\u4e3aik\u3002 <\/p>\n

\u7136\u540e <\/p>\n

\"2{ZG3]DGU8PR2S[9@K%9TX1\"<\/a><\/p>\n

\u4e5f\u4fbf\u662fst [ i ] .. st [ m ]\u4e2d\uff0cst[ i ]\u662fbe\uff0c\u7684\u8303\u5f0f-ik\u7684\u4e2a\u6570\u3002 <\/p>\n

\u53ef\u4ee5\u5f97\u5230\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\uff1a <\/p>\n

\n

1) \u82e5st [ i ] = be\u6216\u8005 st [ i ] = 0\u90a3\u4e48\uff0c<\/p>\n

\"image\"<\/a> <\/p>\n

2) \u5426\u5219\uff0c <\/p>\n

f [ i , be , ik ] = 0<\/p>\n<\/blockquote>\n

\u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u5728O ( m * 4^2 * k ) \u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5185\u7b97\u51fa\u6240\u6709\u7684f\u548csum\u3002 <\/p>\n

\u7136\u540e\u6211\u4eec\u4ece\u5934\u5f80\u540e\u626b\uff0c\u5bf9\u7b2ci\u4f4d\u7f6e\u4e2a\u4f4d\u7f6e\uff0c\u4ece1\u52304\u679a\u4e3ebe, \u82e5\u53d1\u73b0sum[ i , be , K ] < R, \u5c31\u8868\u660e\u5728\u8fd9\u4e2a\u4f4d\u7f6e\u586b\u8fd9\u79cd\u6838\u82f7\u9178\u4e0d\u80fd\u8fbe\u5230\u7ed3\u679c\u3002\u6240\u4ee5\u5c31 r := r \u2013 sum[ i , be, k ] , \u82e5be\u5c0f\u4e8ei-1\u5904\u586b\u7684\u6838\u82f7\u9178\uff0c\u90a3\u4e48\u4fbf k := k \u2013 1 \u3002 \u5982\u679csum[ i , be , K ] >= R , \u5c31\u8868\u660e\u8fd9\u4e2a\u4f4d\u7f6e\u5e94\u8be5\u586bbe\u4e86\uff0c\u4fbf\u53bb\u5904\u7406\u7b2ci + 1\u4e2a\u4f4d\u7f6e\u4e86\u3002 <\/p>\n

\u6211\u7684\u7a0b\u5e8f\uff1a <\/p>\n

{
ID: sinya1
PROG: dna
LANG: PASCAL
} <\/p>\n

uses math; <\/p>\n

const
  code:array[‘A’..’T’]of longint=(1,0,2,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,4);
  decode:array[1..4]of char=(‘A’,’C’,’G’,’T’);
  maxm=50000;
  maxl=maxm;
  maxk=9; <\/p>\n

var
  m,k,i,be,next,ik,up,down:longint;
  st:array[0..maxm]of longint;
  ch:char;
  f,sum:array[1..maxm+1,1..4,0..maxk]of int64;
  r:int64; <\/p>\n

procedure init;begin
  readln(m,k,r);dec(k);
  for i:=1 to m do begin
    read(ch);st[i]:=code[ch];
  end;
  st[0]:=1;
end; <\/p>\n

procedure dp;begin
  fillchar(f,sizeof(f),0);
  fillchar(sum,sizeof(sum),0);
  f[m+1,4,0]:=1;
  for i:=m downto 1 do begin
    if st[i]>0 then begin
      up:=st[i];down:=up;
    end else begin
      up:=4;down:=1;
    end;
    for be:=down to up do begin
      for ik:=0 to k do
        for next:=be to 4 do
          f[i,be,ik]:=f[i,be,ik]+f[i+1,next,ik];
      for ik:=1 to k do
        for next:=1 to be-1 do
          f[i,be,ik]:=f[i,be,ik]+f[i+1,next,ik-1];
      sum[i,be,0]:=f[i,be,0];
      for ik:=1 to k do
        sum[i,be,ik]:=sum[i,be,ik-1]+f[i,be,ik];
    end;
  end;
end; <\/p>\n

procedure find;begin
  for i:=1 to m do begin
    dec(k);
    for be:=1 to 4 do begin
      if be=st[i-1] then inc(k);
      if sum[i,be,k]>=r then break
      else r:=r-sum[i,be,k];
    end;
    st[i]:=be;
    write(decode[st[i]]);
  end;
  writeln;
end; <\/p>\n

begin
  assign(input,’dna.in’);reset(input);
  assign(output,’dna.sol’);rewrite(output); <\/p>\n

  init;
  dp;
  find; <\/p>\n

  close(input);close(output);
end.<\/p>\n","protected":false},"excerpt":{"rendered":"

\u9898\u76ee\u4e0e\u6570\u636e\u79fb\u6b65APIO\u5b98\u65b9\u7f51\u7ad9\uff1ahttp:\/\/www.apio.olympiad.org\/ \u9996\u5148\u6211\u5bf9ACGT\u5206 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[23,131,344],"class_list":["post-436","post","type-post","status-publish","format-standard","hentry","category-13","tag-apio","tag-131","tag-344"],"_links":{"self":[{"href":"https:\/\/sinyalee.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/436","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sinyalee.com\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sinyalee.com\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sinyalee.com\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sinyalee.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=436"}],"version-history":[{"count":0,"href":"https:\/\/sinyalee.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/436\/revisions"}],"wp:attachment":[{"href":"https:\/\/sinyalee.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=436"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sinyalee.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=436"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sinyalee.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=436"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}